High harmonic generation (HHG) of intense infrared laser radiation (Ferray et al., J. Phys. B: At. Mol. Opt. Phys. 21:L31, 1988; McPherson et al., J. Opt. Soc. Am. B 4:595, 1987) enables coherent vacuum-UV (VUV) to soft-X-ray sources. In the usual setup, energetic femtosecond laser pulses are strongly focused into a gas jet, restricting the interaction length to the Rayleigh range of the focus. The average photon flux is limited by the low conversion efficiency and the low average power of the complex laser amplifier systems (Keller, Nature 424:831, 2003; Sudmeyer et al., Nat. Photonics 2:599, 2008; Roser et al., Opt. Lett. 30:2754, 2005; Eidam et al., IEEE J. Sel. Top. Quantum Electron. 15:187, 2009) which typically operate at kilohertz repetition rates. This represents a severe limitation for many experiments using the harmonic radiation in fields such as metrology or high-resolution imaging. Driving HHG with novel high-power diode-pumped multi-megahertz laser systems has the potential to significantly increase the average photon flux. However, the higher average power comes at the expense of lower pulse energies because the repetition rate is increased by more than a thousand times, and efficient HHG is not possible in the usual geometry. So far, two promising techniques for HHG at lower pulse energies were developed: external build-up cavities (Gohle et al., Nature 436:234, 2005; Jones et al., Phys. Rev. Lett. 94:193, 2005) and resonant field enhancement in nanostructured targets (Kim et al., Nature 453:757, 2008). Here we present a third technique, which has advantages in terms of ease of HHG light extraction, transverse beam quality, and the possibility to substantially increase conversion efficiency by phase-matching (Paul et al., Nature 421:51, 2003; Ren et al., Opt. Express 16:17052, 2008; Serebryannikov et al., Phys. Rev. E (Stat. Nonlinear Soft Matter Phys.) 70:66611, 2004; Serebryannikov et al., Opt. Lett. 33:977, 2008; Zhang et al., Nat. Phys. 3:270, 2007). The interaction between the laser pulses and the gas occurs in a Kagome-type Hollow-Core Photonic Crystal Fiber (HC-PCF) (Benabid et al., Science 298:399, 2002), which reduces the detection threshold for HHG to only 200 nJ. This novel type of fiber guides nearly all of the light in the hollow core (Couny et al., Science 318:1118, 2007), preventing damage even at intensities required for HHG. Our fiber guided 30-fs pulses with a pulse energy of more than 10 mu J, which is more than five times higher than for any other photonic crystal fiber (Hensley et al., Conference on Lasers and Electro-Optics (CLEO), IEEE Press, New York, 2008).